4. Suppose P(A) = 0.48 and P(B) = 0.62. a. Can A and B be mutually exclusive? Why or why not. b. If A and B are independent, then what is the probability of both A and B occurring? c. Can A and B be mutually exclusive events and be independent events at the same time?

Step-by-step explanation:

a) Two events A,B are said to be mutually exlusive if any of the following occurs.

- A and B have an empty intersection

- A= B^c and their union is the whole sample space

- P(A intersection B) =0

REcall the following formula

Note that P(A) + P(B) = 1.1. Since the probability is always a number between 0 and 1, it must happen that , otherwise, would have a probability greater than 1. Hence, A, B are not mutually exclusive.

b) by definition, if two events are indepent, we have that the probability of the intersection is equal to products of their probabilites. Or

c) Recall that if we have mutuallly exclusive events A, B, then we have that  , if they were independent, we would have the following

which necesarilly implies that at least one of the two events has 0 probability. (THis is not the case)

over the argument its not good to fight.

the 2 figures are congruent bc if you reflect abcd over the y axis then over the d axis the figures overlap